Usually I just fix it, because I think of it this way: the amount of time I'll spend fixing this is (usually) trivial compared to the amount of time they'll waste trying to fix it - if I'm someone's friend, and I can take 10 minutes out of my day to fix something that they would struggle with for an hour or two and make their life a little better, shouldn't I do it? Today you, tomorrow me.
That being said, I'm not particularly bombarded by these kinds of requests and I could definitely see it wearing on me if people were constantly asking me to fix their machines.
It depends, though. I've found that sometimes people can use me as a crutch and don't even try to fix it themselves before coming to me. And other times it's better to teach them how to find the solution to that type of problem than to just fix it for them.
So, yeah, I sort of agree with you, but the math can get more complicated. If it's me fixing it for them x 10 vs. them taking an hour to figure it out, then the first option might be more efficient and more gratifying.
If they're on Windows, I send them to www.ninite.com to get antivirus, anti-malware, and Firefox to browse with. All their selections will be packaged into a single, slick installer by the site. This handles a lot of problems. I often have them do it themselves while I supervise. This reduces dependency.
I don't mind doing it for family or close friends, but if it is some tangentially related person I tell them I charge $90 an hour. This really cuts down on the leechers, and you'd be surprised how many people will actually pay you.
p.s. I came up with this rate because it's the same amount that the local Subaru race shop charges to work on your car.
I don't mind fixing some friends' computers. I draw the line when they are running a pre-2001 computer with 2011 software in, you guessed it, 2011. My family is incredibly frugal so they don't understand why a computer from 2000 is now slow, and that buying a new one would fix their problem.
I'm surprised at how bitter those responses are. Of course I will help friends and family with their computer problems -- they are my friends and my family! When I run into trouble and need their help I would hope they'd be there for me...
Generally, doing it for friends and family shouldn't be a problem. Occasionally though people expect miracles, they expect them fast, and they're pretty ungrateful.
It's also easy to be sucked in by acquaintances like this: "Can you have a look at my PC after work? It won't take very long and I'll make you dinner." to which you of course agree. The bad part comes later, because you've just set a precedent and evenings like this will keep repeating. Those people think two afterwork hours of fiddling with their ancient Windows crap is worth exactly one burrito and a Sprite. Yeah, it happened to me recently.
"What's a computer? Is that like a copier? I tried to fix one of those once and then this black stuff went everywhere. Yeah, and it doesn't really come out of carpet, either!"
That being said, I'm not particularly bombarded by these kinds of requests and I could definitely see it wearing on me if people were constantly asking me to fix their machines.